What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge?

Given that the quarks have the fractional electric charges they do, this is a consequence of color confinement. The charges of the quarks are constrained in the context of the standard model by anomaly cancellation, and can be explained by grand unification. The GUT explanation for the charges doesn't care about the bound state spectrum of the QCD sector, so it just seems to be a coincidence that hadrons (which are composite) have integer charge, and that leptons (which are elementary) also have integer charge.

Now maybe there's some anthropic argument for why such a coincidence is useful (in the case of proton and electron, it gives us atoms as we know them). Or maybe you can argue that GUTs naturally produce fractionally charged particles and strongly coupled sectors, and it's just not much of a coincidence.

But I remain curious as to whether Seiberg duality, anyons, some UV/IR relationship... could really produce something like the lepton-hadron charge coincidence, for deeper reasons. I suppose one is looking for a theory in which properties of bound states in one sector have a direct and nontrivial relationship to properties of elementary states in another sector. Is there anything like this out there?

(This question was prompted by muster-mark's many recent questions about fractional charge, and by a remark of Ron Maimon's that the hadron-lepton charge coincidence is a "semi-coincidence", which assured me that I wasn't overlooking some obvious explanation.)

Seems to me that the comment of Ron you link to points to the answer: that it is QED constraints that need integer leptons and baryons?
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anna vSep 24 '12 at 3:33

Isn't this just group theory? Anomaly cancellation fixes the charges of quarks, and color SU(3) fixes the charges of color singlet hadrons. Also note that the hypercharge assignments that lead to anomaly cancellation are essentially unique.
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ThomasSep 24 '12 at 17:21

@Thomas: it doesn't fix the charges uniquely, it fixes it up to multiples, and there's a question of why it turns out that all singlets are integer charged. If you add fractionally charged stronly interacting scalars, for instance, the integer charge is out the window.
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Ron MaimonSep 25 '12 at 8:51

2 Answers
2

The simplest answer to your question is a quite old idea, captured best I think by the Rishon model of Haim Harari, Michael Shupe, Nathan Seiberg, and others.

Their answer is the simple and rather obvious one: Hadrons and leptons have identical charge because they are composed out of the same set of more fundamental particles and anti-particles, specifically an uncharged V particle and a one-third charged T particle.

Alas, in terms of mathematical development the Rishon model is more akin to an intriguing speculation than a fully developed and predictive physics model. I do not personally think that any particle-based version of the Rishon model can ever be made to work. My suspicion is that theories like the Rishon model are best viewed as incomplete and distorted images of some far less obvious form of composition, one with components that conserve certain properties but cannot be called particles in any traditional meaning of the word.

Nonetheless, the Rishon model strikes me as orders of magnitude better than some of the more recent trends to explain issues such as electron-proton charge equality by invoking what amounts to anthropic self-selection gone wild. Why? Because Rishon theory at least tries to explain astonishing coincidences. If Newton had given up so easily on looking for deeper roots behind an effect as infinitely precise and in-your-face obvious as electrons and protons have identical charge magnitudes, we'd still be talking about how amazing and lovely it is that Great Angels push the planets around in patterns too lofty and subtle for humans ever to understand.

2012-09-27 Addendum

Here's a point I should make clear for the record, since I came down pretty heavy on the idea that evolving universes could create balanced sets of charges via nothing more than the anthropic principle.

The anthropic observation that the existence of life as we know it seems to require that many fundamental constants to be very tightly constrained and balanced with each other is a simply delightful observation that truly needs explanation. Simple examples include such things as the remarkably long an sharp ridge of stable isotopes that enable complex chemistry, nuclear fusion suitable for stars, and the ability of carbon (with nitrogen and other helpers) to form indefinitely long stable chains. These applications of the anthropic principle are all in effect fine-tuning issues, and I think they are entirely legitimate issues for applying your own personal favorite version of anthropic selection if you are so inclined.

Where I have deep heartburn is with the far more radical versions of the idea that essentially toss all aspects of physics into one big mysterious anthropic pot that then magically burps out whatever it is you need to make life possible. If that is true, why do physics and chemistry constantly throw unexpected structure and marvelous little symmetries in our faces, in even a cursory look? Wouldn't a true, unbiased anthropic cauldron simply toss out a universe that works fine for life, but shows no unnecessary correlations or symmetries between the resulting diverse components of its physics? Such patterns and correlations would after all represent an unnecessary, irrational, and mechanistically inexplicable "extra effort" on the part of the anthropic cauldron, an effort that goes far beyond what is needed simply to enable life. If you own a true anthropic cauldron, Occam's razor says "why bother?" with anything more in the product.

Or stated another way: I have no problem with using anthropic ideas to adjust the ratio between two tightly meshed gears, but I have a lot of trouble with using it to create the gears themselves. Nearly every finding in physics seems to be shouting at us that the bones and tendons of the universe arise from complex permutations and various degrees of breaking of symmetries, with many of details of those symmetries and their permutations being being captured at least partially in that marvelous work called the Standard Model.

So, my real message on this issue is a simple one: Extreme applications of otherwise good ideas tend to be wrong, often rather spectacularly so. Exclusion of extremes is a nicely general principle that applies to a very wide range of phenomena, and I just can't see any good reason why the anthropic principle should get a waiver from it.

This is not correct--- the rishon idea is not any better than just the standard model regarding this question--- you might as well ask why is it that the rishons that are not confined have the same integer multiples as the rishons that make the leptons. The rishon model does not explain this thing.
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Ron MaimonSep 25 '12 at 8:50

I wasn't critiquing the standard model. It's been seriously postulated that the identical charges of electrons and quark-composed protons are just the result of self-selection among evolving universes, and thus have no deeper explanation than the need for matching values to enable us to be here to observe them. If you accept the premise of physics of the 1800s and early-to-mid 1900s that there is deep and profound simplicity underlying the apparent complexity in physics (and I do), then simple composition easily beats such extreme versions of anthropic evolutionary universe selection.
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Terry BollingerSep 25 '12 at 14:18

Except it's not any simpler to have integer charged hadrons, you have fractional charged hadrons in models no more complex than the usual ones. there is no real relation between the quarks and leptons other than anomaly cancellation or coming from a GUT. The major thing that would happen with a fractionally charged hadron is that there would be a stable lightest one and it would affect cosmology, it wouldn't be complicated, just wrong.
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Ron MaimonSep 25 '12 at 16:07

I do not see the need to search further for why the three quarks add up to the electron charge than that given by the group structure of the Standard Model. The SM is very successful in organizing into beautiful symmetries the particle and resonances data gathered the last sixty years or so. There is no experimental reason to assume further layers of compositness defining a "deeper" group structure from which the "measured" SU(3)xSU(2)xU(1) should emerge. It will just introduce a lower level of unnecessary complexity.

If what intrigues you is the unit one, after all we can always say the down quark has charge -1, the up quark 2 and the electron -3. The group symmetries are the same and we will have a generic unit 1 .